Lattice is a way of discretizing a quantum field theory for numerical simulations.

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What evidence do we have for S-duality in N=4 Super-Yang-Mills?

Do we have anything resembling a proof*? Or is it just a collection of "coincidences"? Also, do we have evidence from lattice gauge theory computations? *Of course I'm not talking about a proof in ...
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Are there rigorous constructions of the path integral for lattice QFT on an infinite lattice?

Lattice QFT on a finite lattice* is a completely well defined mathematical object. This is because the path integral is an ordinary finite-dimensional integral. However, if the lattice is infinite, ...
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211 views

Why is the crystallography restriction obeyed?

The crystallography restriction states that any 2-dimensional lattice can have rotational symmetry of degree 1, 2, 3, 4 or 6 - and that's it. A simple proof of I've heard of this is: the magnitude of ...
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787 views

Continuum theory from lattice theory

I am looking for references on how to obtain continuum theories from lattice theories. There are basically a few questions that I am interested in, but any references are welcome. For example, you can ...
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417 views

Why can't we set the lattice spacing 'a' in lattice QCD?

My question is to do with lattice QCD. In the lattice action there is a parameter, 'a', the lattice spacing in physical units. However, if we want to generate a configuration with a certain lattice ...
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What is the fundamental reason of the fermion doubling?

Recall that the fermion doubling is the problem in taking the $a \to 0$ limit of a naively discretized fermionic theory (defined on a lattice with lattice spacing $a$). After such a limit one finds ...
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Lattice QCD and the 5th dimension

I was digging into the Nielsen-Ninomiya Theorem and doubler fermions, as well as solutions to these problems using Domain Wall Fermions and overlap lattice fermions, both of which make effective use ...
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5answers
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Home-made lattice calculation?

The topic of Lattice QCD or Lattice gauge theory or even Lattice field theory is quite old now. And the main reason for the interest in the topic is the ability to calculate nonperturbative stuff on a ...
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1answer
201 views

Convergence of periodic single fermion operators

First, a quick remark: I'm a mathematician, now working on some problems coming from physics (in particular Ising models on quasiperiodic chains). A few things I find rather mysterious. I would ...
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Why is high temperature superconductivity so hard to solve?

The phenomenon of high temperature superconductivity has been known for decades, particularly layered cuprate superconductors. We know the precise lattice structure of the materials. We know the band ...
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689 views

Is anyone studying how the general topology of spacetime arises from more fundamental notions?

Stephen Wolfram in his book A New Kind of Science touches on a model of space itself based on automata theory. That it, he makes some suggestions about modelling not only the behaviour of matter ...
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692 views

Lattice QCD and string theory

I've heard the claim that some aspects of string theory are used to improve Monte-Carlo simulations of lattice QCD, for example by people working at the LHC. I know a bit about Monte-Carlo methods in ...
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213 views

Why do regular lattice elements heat up faster?

For example iron. A metal spoon heats up much quicker than a wooden/plastic one. Why?
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333 views

What is known about some massive Gaussian models on a lattice?

Recently I started to play with some massive Gaussian models on a lattice. Motivation being that I work on massless models and want to understand the massive case because it seems easier to handle ...